Is there a way to find out where a military duty station is by the APO
or FPO address?

Dear angelica1-ga,

The Military Post Office Location List can be downloaded on this link.
http://www.dtic.mil/whs/directives/corres/pdf/45256l1_0290/p45256l1.pdf
This is obtained from the Department of Defense directives.
http://www.dtic.mil/whs/directives/


An alternative is to search the Military Installation Guide on this
site. Their search engine does not allow one to search by code, but
use the format below in Google (this example is for 09139), it will
bring up the relevant page.
http://benefits.military.com/misc/installations/Browse_Service.jsp

site:benefits.military.com 09139
://www.google.com/search?sourceid=navclient-ff&ie=UTF-8&rlz=1B2GGGL_enGB177&q=site:benefits.military.com+09139

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder